Q: What are the factor combinations of the number 30,981,005?

 A:
Positive:   1 x 309810055 x 619620111 x 281645555 x 563291167 x 185515835 x 371031837 x 168653373 x 9185
Negative: -1 x -30981005-5 x -6196201-11 x -2816455-55 x -563291-167 x -185515-835 x -37103-1837 x -16865-3373 x -9185


How do I find the factor combinations of the number 30,981,005?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 30,981,005, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 30,981,005
-1 -30,981,005

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 30,981,005.

Example:
1 x 30,981,005 = 30,981,005
and
-1 x -30,981,005 = 30,981,005
Notice both answers equal 30,981,005

With that explanation out of the way, let's continue. Next, we take the number 30,981,005 and divide it by 2:

30,981,005 ÷ 2 = 15,490,502.5

If the quotient is a whole number, then 2 and 15,490,502.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 30,981,005
-1 -30,981,005

Now, we try dividing 30,981,005 by 3:

30,981,005 ÷ 3 = 10,327,001.6667

If the quotient is a whole number, then 3 and 10,327,001.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 30,981,005
-1 -30,981,005

Let's try dividing by 4:

30,981,005 ÷ 4 = 7,745,251.25

If the quotient is a whole number, then 4 and 7,745,251.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 30,981,005
-1 30,981,005
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

1511551678351,8373,3739,18516,86537,103185,515563,2912,816,4556,196,20130,981,005
-1-5-11-55-167-835-1,837-3,373-9,185-16,865-37,103-185,515-563,291-2,816,455-6,196,201-30,981,005

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